limit

the final, utmost, or furthest boundary or point as to extent, amount, continuance, procedure, etc.:

the limit of his experience; the limit of vision.

2.

a boundary or bound, as of a country, area, or district.

3.

Mathematics.

a number such that the value of a given function remains arbitrarily close to this number when the independent variable is sufficiently close to a specified point or is sufficiently large. The limit of 1/ x is zero as x approaches infinity; the limit of (x − 1) 2 is zero as x approaches 1.

a number such that the absolute value of the difference between terms of a given sequence and the number approaches zero as the index of the terms increases to infinity.

one of two numbers affixed to the integration symbol for a definite integral, indicating the interval or region over which the integration is taking place and substituted in a primitive, if one exists, to evaluate the integral.

4.

limits, the premises or region enclosed within boundaries:

We found them on school limits after hours.

5.

Games. the maximum sum by which a bet may be raised at any one time.

6.

the limit, Informal. something or someone that exasperates, delights, etc., to an extreme degree:

You have made errors before, but this is the limit.

verb (used with object)

7.

to restrict by or as if by establishing limits (usually followed by to):

c.1400, "boundary, frontier," from Old French limite "a boundary," from Latin limitem (nominative limes) "a boundary, limit, border, embankment between fields," related to limen "threshold." Originally of territory; general sense from early 15c. Colloquial sense of "the very extreme, the greatest degree imaginable" is from 1904.

(lĭm'ĭt) A number or point for which, from a given set of numbers or points, one can choose an arbitrarily close number or point. For example, for the set of all real numbers greater than zero and less than one, the numbers one and zero are limit points, since one can pick a number from the set arbitrarily close to one or zero (even though one and zero are not themselves in the set). Limits form the basis for calculus, where a number L is defined to be the limit approached by a function f(x) as x approaches a if, for every positive number ε, there exists a number δ such that |f(x)-L| < ε if 0 < |x-a| < δ.